Here's another way to get out there that doesn't involve hiking. Go someplace where you can rent a canoe, or borrow one. Put your gear in it, canoe till you find a nice spot, and camp there.
Canoe camping is great. You can get to that island when everyone else camps on the shore. The weight of your gear is immaterial. You can take an ice-chest with fresh food and cold drinks.
Canoeing is easy - but start slow, DO NOT GO 8 MILES IN ON YOUR FIRST TRIP. Since you are around water, bug nets and repellent are required. You can fish. You can carry firewood to an area with none and have a fire there. You can attach your GPS to a thwart for real time navigation. Oh and sunscreen for the reflected sunlight off water. Be sure to pull the canoe up onto dry land so its still around when you want to leave.
My wife hates to BP, but loves to canoe camp - think about it...